Related papers: On the Borel-Cantelli Lemma
In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.
We prove several generalisations of the ping-pong lemma for negatively curved groups.
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
We study the dynamical Borel-Cantelli lemma for recurrence sets in a measure preserving dynamical system $(X, \mu, T)$ with a compatible metric $d$. We prove that, under some regularity conditions, the $\mu$-measure of the following set \[…
We introduce partially lax limits of infinity-categories, which interpolate between ordinary limits and lax limits. Most naturally occurring examples of lax limits are only partially lax; we give examples arising from enriched categories…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of B\"or\"oczky, Lutwak, Yang and Zhang.
We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.
In this small article, unified first law has been analyzed and some results have been deduced from it. The results have been presented in the form of lemmas and some conclusions have been drawn from them.
We study the strong Borel-Cantelli property both for events and for shifts on sequence spaces considering both a conventional and a nonconventional setups. Namely, under certain conditions on events $\Gamma_1,\Gamma_2,...$ we show that with…
We revisit the Bohnenblust--Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of…
We start by giving a survey to the theory of Borel*(\kappa) sets in the generalized Baire space Baire({\kappa}) = {\kappa}^{\kappa}. In particular we look at the relation of this complexity class to other complexity classes which we denote…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of…
The article has been withdrawn by the author. Wolfgang Lueck and Peter Linnell pointed out that the proof of Lemma 3.8 does not apply to the unrestricted case of wreath product. It is not clear at this stage how to complete the proof of…
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
The aim of this paper is to give a proof of improving of Zalcman's lemma.
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…